A comparison of the bounds, beta-approximate, and exact variants of 2 tests for heteroscedasticity based on ordinary least-squares residuals

Abstract

Precis: This paper compares the small sample empirical size, power and incidence of inconclusiveness of the bounds tests for heteroscedasticity proposed by Szroeter (1978) and Harrison and McCabe (1979). It also examines the performance of the exact and beta-approximate variants of the tests. Probabilities are computed numerically using both simulated and actual data and various heteroscedasticity specifications. No consistent power superiority of either test is found, although for the types of heteroscedasticity most commonly postulated in applied economics, Szroeter's test is the more powerful. On the other hand, Szroeter's test suffers from the higher incidence of inconclusiveness in all of the cases examined. Two-moment beta-approximations perform well compared with the exact tests. An example of the use of both bounds tests is given.